We present two sets of three-dimensional numerical models of non-ideal magneto- hydrodynamic (MHD) turbulence, one relevant to star formation in molecular clouds and the other to planet migration in protostellar disks. All nascent stars are found in molecular clouds, and observations of these clouds reveal turbulent motion through supersonic linewidths and magnetic fields with energies near equipartition. Molecular clouds have very low densities and ionization fractions, and so the magnetic field (and ions tied to it) and neutrals are not well coupled. The resulting drift is referred to as ambipolar diffusion, and it acts as a non-linear diffusion for magnetic fields. In the turbulent theory of star formation, the dense cores that collapse to become stars are formed out of the turbulent cascade. We calculate numerical models of driven MHD turbulence with ambipolar diffusion (AD) terms and find that AD does not truncate the turbulent cascade. In the context of star formation, we show that it therefore cannot set a mass scale for the gravitational collapse of star forming cores. Planets form in accretion disks thought to be driven by turbulence. The most widely considered source of turbulence in disks is the magnetorotational instability (MRI). However, protoplanetary disks have cold, dense midplanes with low ionization fractions that cannot sustain the MRI. This "dead zone" is a likely site of planet formation. We simulate a region of a disk using the stratified shearing-box, including a height-dependent resistivity that generates a dead zone. We monitor the torques on a protoplanet caused by turbulent over-densities and find them to have a time-stationary distribution and finite correlation time. These results suggest stochastic methods can be used to study the orbital distributions of large populations of forming protoplanets, and we derive the diffusion coefficient for such methods. Finally, we characterize the motions in the dead zones driven by the MRI turbulence in active layers at high altitudes in the disk. Although the MRI provides significant amounts of vorticity, we find no evidence for vortices that survive for appreciable periods. However, a number of distinct wave modes are found, including one peculiar to dead zones.